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Available from: 

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Acknowledgments 

The authors wish to acknowledge Noah Schiller, Randolph H. Cabell and Jacob Klos of 

the NASA Langley Research Center for their assistance with the equalization filter 

development, and William L. Chapin of AuSIM, Inc. for the Vectsonic system 

development support. 

This research was supported by an appointment to the NASA Postdoctoral Program at the 

NASA Langley Research Center, administered by Oak Ridge Associated Universities 

(ORAU) through a contract with NASA. Funding was provided by the Subsonic Rotary 

Wing project of the NASA Fundamental Aeronautics Program. 

Trade names and trademarks are used in this report for identification only. Their usage does not constitute 

an official endorsement, either expressed or implied, by the National Aeronautics and Space 

Administration. 
1 

Abstract 

The Exterior Effects Room (EER) is a 39-seat auditorium at the NASA Langley Research Center and 

was built to support psychoacoustic studies of aircraft community noise. The EER has a real-time 

simulation environment which includes a three-dimensional sound-reproduction system. This system 

requires real-time application of equalization filters to compensate for spectral coloration of the sound 

reproduction due to installation and room effects. This paper describes the efforts taken to develop the 

equalization filters for use in the real-time sound-reproduction system and the subsequent analysis of the 

system’s acoustic performance. The acoustic performance of the compensated and uncompensated soundreproduction system is assessed for its crossover performance, its performance under stationary and 

dynamic conditions, the maximum spatialized sound pressure level it can produce from a single virtual 

source, and for the spatial uniformity of a generated sound field. Additionally, application examples are 

given to illustrate the compensated sound-reproduction system performance using recorded aircraft 

flyovers. 
2 

Contents 

1 Introduction 3

2 VBAP Implementation in the EER 6

3 Equalization Filters 8

3.1 Ideal Equalization Filters 9

3.2 Wiener Equalization Filters 9

3.3 IIR Equalization Filters 10

4 Time-Delay and Gain Compensation 12

4.1 Time-Delay Compensation 12

4.2 Relative Gain Compensation 13

5 Acoustic Performance 14

5.1 Crossover Performance 14

5.2 Stationary Performance 15

5.3 Dynamic Performance 16

5.4 Maximum Spatialized SPL 17

5.5 Spatial Uniformity 18

6 Application Examples 19

7 Concluding Remarks 20

8 Appendix - Installed Speaker Locations 21

9 References 22
3 

1 Introduction 

The primary function of the Exterior Effects Room (EER) is to conduct psychoacoustic studies of 

aircraft community noise [1–6]. A secondary function of the EER is as a general meeting space (e.g., 

presentations). The EER sound-reproduction system was originally only capable of reproducing monaural 

playback of pre-recorded aircraft flyovers. In order to achieve a more realistic simulation environment 

using both synthetic and recorded flyovers, a real-time three-dimensional (3D) sound-reproduction system 

was recently installed. The new 31-channel sound-reproduction system consists of twenty-seven fullrange Klein & Hummel (K&H) O300 satellite loudspeakers and four K&H O900 subwoofer 

loudspeakers. The loudspeakers provide a combined uncompensated frequency range from 16 Hz to 20 

kHz. The subwoofers are embedded in the walls at the corners of the room and the satellites are 

positioned in the half and corner spaces of the room. The satellite loudspeakers located in the lower half 

of the room are baffled to protect the audio equipment and personnel, see Figure 1. Speaker designations 

are also indicated in Figure 1. Three speakers (0.5, 1.5, and 2.5) are located on the room left/right center 

line, with speakers 0.5 and 1.5 at the front of the room and speaker 2.5 in the rear. The remaining 

speakers are located in nominally symmetric locations. Speakers 4L/R, 5L/R, and 6L/R are located in the 

ceiling. Subwoofers 15L/R and 16L/R are embedded in the front and rear walls, respectively. 

The room dimensions are shown in the floor plan in Figure 2. Installed speaker locations relative to 

the center microphone location, at the x-y origin in Figure 2, are provided in the appendix. The center 

microphone location was at a height of 52-in (1.32m) above the lowest floor level at the front of the room. 
4 

Figure 1: Front (a) and rear (b) views of the EER 

showing the mounted satellite and subwoofer speaker locations. 

(a)

(b)

1.5

0.5

3L 3R

8L 8R

15L

15R

9L

9R

10L

11L 10R

11R

12L

12R

13R

4L

5L 5R

4R

7R

2.5

16L

14L

11L 11R

12R

13R

5R 5L

16R

13L

12L

14R

7L

6R 6L
5 

Figure 2: Floor plan of the EER outline (dimensions in feet - inches). 

The sound-reproduction system also includes a real-time Digital Signal Processing (DSP) engine 

which can produce 3D spatial audio in the EER using an implementation of Vector-Base Amplitude 

Panning (VBAP) [7, 8]. VBAP is an extension of the familiar 2D stereo panning technique, which uses a 

pair of loudspeakers to pan a virtual source (Figure 3a). With VBAP, the virtual source can be panned in 

three dimensions. For VBAP, a triangular panning area is formed by a loudspeaker triplet and a virtual 

source is panned within this area by manipulating the gains of the loudspeakers (Figure 3b). If more than 

three loudspeakers are available, then a set of non-overlapping triangles are formed between the 

loudspeakers and a virtual source can be panned within this triangle set (see Figure 3c). The VBAP 

implementation used in the EER is discussed in Section 2. 

Figure 3: Stereo and VBAP loudspeaker arrangements for, a) a stereo pair, b) a single triplet and, c) multiple triplets (3D 

head, shoulder, and chest model by [9]).

The arrangement of the loudspeakers in the EER is non-spherical and the EER itself is non-anechoic. 

Hence, loudspeaker-specific equalization is necessary to compensate for the spectral colorization, time 

delay, and gain resulting from these non-ideal acoustic conditions. In addition, crossover filters are 

needed to split the audio signal(s) into lower and higher frequency bands which are subsequently routed 

to the respective subwoofer and satellite loudspeakers. The DSP required of the real-time system thus 

x

y

RIGHT

LEFT

FRONT

CL

REAR

5’-6”
6 

involves both dynamic VBAP gain application for moving virtual sources, and fixed filter, time delay and 

gain processing for equalization, as depicted in Figure 4. The DSP for VBAP is performed using the 

AuSIM3D® VectsonicTM option for the AuSIM3D® Engine [10], which also performs the remaining DSP 

for equalization. 

Figure 4: Real-time digital signal processing path for the EER sound-reproduction system. Dynamic gain and fixed 

equalization are performed for all 31 channels at all times. 

The remainder of the paper describes the VBAP implementation used in the EER, the design and 

implementation of fixed equalization for the EER sound-reproduction system, including equalization 

(color compensation and crossover) filters, full-path time delay compensation, and relative gain 

compensation between loudspeakers. The acoustic performance is then demonstrated under various 

uncompensated and compensated conditions. 

2 VBAP Implementation in the EER 

The gain factors used to position a virtual source p within a speaker triangle set (ln, lm, lk) are 

determined by the geometrical relationship of the listener to the speaker set and virtual source [7, 8], see 

Figure 3b. Given the loudspeaker direction vectors, 

 [ ]

 

 [ ]

 

 [ ]

 

 [ 

]

 

(1)

and the panning direction vector 

 [ 

]

 (2)

the gain factors are obtained as 

 [ 

]

 

 (3) 

For the EER system, the gain factors are pre-computed for a large but finite number of virtual sources 

at regularly spaced grid points within the triangle and intermediate locations are estimated during runtime 

using interpolation. Two separate VBAP triangle sets are used in the EER: one for the satellite 

loudspeakers and one for the subwoofer loudspeakers. Both sets are shown in Figure 5. 

During the installation of the 3D sound reproduction system, it was decided to utilize existing 

penetrations in the ceiling for mounting loudspeakers 4 L/R, 5L/R and 6 L/R. As a consequence, the 

triangle sets defined by these loudspeakers were not unique. Specifically, for the quadrilateral defined by 

loudspeakers 4 L/R and 5 L/R, triangle sets 4L-4R-5R and 4L-5L-5R are equally as valid as triangle sets 

4L-4R-5L and 4R-5L-5R (see Figure 5a). Similarly, for the quadrilateral defined by loudspeakers 5L/R 

and 6 L/R, triangle sets 5L-5R-6R and 5L-6L-6R are equally as valid as triangle sets 5L-5R-6L and 5R6L-6R. Selection of one triangle set over the other leads to sudden and perceivable level changes in the 

sound reproduction as a virtual source was panned across these sets [11]. To resolve this issue, virtual 

loudspeakers were positioned between loudspeakers 4 L/R and 5 L/R, and between loudspeakers 5 L/R 

and 6 L/R, as shown in Figure 5a. A virtual loudspeaker is a means of specifying a loudspeaker direction 

vector for a point at which there is no physical loudspeaker, see equation (1). The gain attributed to the 
7 

virtual loudspeaker is then apportioned equally amongst the neighboring physical loudspeakers. For 

example, a virtual source located in the triangle defined by loudspeakers 4 L/R and the virtual 

loudspeaker between loudspeakers 4L/R and 5 L/R would produce the following physical loudspeaker 

gains: 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(4)

where the superscript V denotes the VBAP gain obtained for the triangle defined by loudspeakers 4 L/R 

and the virtual loudspeaker. The use of virtual loudspeakers on the ceiling was found to eliminate the 

perceived level changes for virtual sources panned between loudspeakers 4 L/R, 5 L/R, and 6 L/R. 

A virtual loudspeaker was also used to conditionally replace a physical loudspeaker. The EER 

contains a 3D visual system that requires a projection screen which, when lowered, obstructs loudspeaker 

0.5 directly in front of the EER. Equalization could not adequately overcome the resulting coloration, 

causing an audible high frequency attenuation as a source was panned through the corresponding 

triangles. Improved sound reproduction was achieved by replacing loudspeaker 0.5 with a virtual 

loudspeaker consisting of loudspeakers 1.5-3L-3R-8L-8R, as shown in Figure 5b/c. The appropriate 

triangle set, i.e. with or without the virtual loudspeaker, is loaded at runtime depending on the position of 

the screen. 

A third application of virtual loudspeakers was implemented for the subwoofers. As will be discussed 

in section 3.2, the subwoofers were low-pass filtered so that their output would not be localized. The 3D 

localization achieved with the EER sound reproduction system is thus attributable to the satellite 

loudspeakers alone. The option of simply sending 1⁄4 of the full low-pass filtered signal to each of the four 

subwoofers was not possible due to the DSP system architecture. All loudspeakers, satellites and 

subwoofers, were processed using the same DSP, inclusive of VBAP. Since the subwoofers lie on the 

plane defined by 15L-15R-16L-16R, it is necessary to place virtual speakers above and below that plane 

for the VBAP algorithm to reproduce any sound off-plane, which is most commonly the case. The 

triangle sets shown in Figure 5d are used for this purpose. In this manner, all four subwoofers are active, 

albeit with different gains, at all times.
8 

Figure 5: VBAP triangle sets for the satellite (a-c) and subwoofer (d) speakers in the EER. 

3 Equalization Filters 

Each channel of the EER sound reproduction system, being unique in its installation, must be 

individually equalized. The basic concept behind this equalization is shown in block diagram form in 

Figure 6. The digital equalization filter (H(z)) is used to compensate the input signal (x(n)) such that the 

error (e(n)) between the microphone response(s) ( ̂ ) and the desired response (d(n)) is either 

eliminated or minimized. 

Figure 6: Equalization problem of the sound reproduction system. 
9 

The microphone response(s) ( ̂ ) can be measured at a single microphone location or at multiple 

microphone locations. When equalizing at a single microphone location, it has been shown that 

degradation of the response can occur at other positions. Improvement can be achieved by using the sum 

of square of the modeling error (e(n)) at multiple microphone locations [12] as the cost function. Two 

microphone configurations were considered in this effort; a set of twelve microphones randomly 

positioned within the seating area of the EER, or a two microphone subset located in the center of the 

room. The microphone arrangement is visible in Figure 1. 

3.1 Ideal Equalization Filters 

Ideal equalizers can be obtained from the exact inverse of the frequency responses of the digital filter 

representation of the sound-reproduction system response (G(z)). Theoretically, zero error can be 

achieved with an ideal equalizer and model of the delay (z

-Δ

) introduced in the acoustic path. However, it 

is known that ideal equalizers only work in offline simulations. Even for a simple point-to-point 

reproduction path, response measurement accuracy limitations and minor non-stationarity of the path 

make ideal equalization impossible [13]. In fact these ideal EQs were found to produce audible artifacts, 

specifically a “ringing” artifact, when employed in the EER. 

3.2 Wiener Equalization Filters 

Elliot and Nelson [14] posed the equalization problem as one of linear optimum filtering or Wiener 

filtering. This approach minimizes the error between the microphone(s) and desired response instead of 

attempting to set the error to zero. It assumes the Wiener equalization filter and the sound-reproduction 

system can be represented by digital Linear Time Invariant (LTI) filters which allows for the specification 

of the filter by its impulse response. The resulting Weiner finite impulse response (FIR) filter avoids 

sensitivity to frequency bin spacing which occurs with a frequency domain approach. One drawback to 

this approach is that it requires solution of a Toeplitz system of linear equations. Standard methods for 

solving this type of problem, such as Gauss-Jordan elimination, usually requires O(N3) operations [15]. 

This can result in lengthy calculation times and, for large matrices, may require considerable memory 

resources. However, the LTI assumption implies that the sound-reproduction system is time invariant and, 

therefore, equalization filters are precomputed once and then used in the real-time system. Furthermore, 

the complexity of solving a Toeplitz system of linear equations can be reduced significantly to a general 

requirement of O(N2) operations using Levinson-Durbin recursion [15]. 

Figure 7 illustrates the approach used to solve the equalization problem with a Wiener FIR 

equalization filter [12]. This solution is similar to the general equalization approach from Section 3.1

except that the ideal equalizer (H(z)) is replaced with a Wiener FIR equalization filter (HW(z)) and a 

desired filter (K(z)) is introduced. The desired filter is a digital filter used to specify the desired frequency 

response of the equalization filter. In this manner, crossover filters can be incorporated into the 

equalization filters. It is suggested to specify the desired filter as an 8th-order Linkwitz-Riley (L-R) 

crossover filter because interactions at the crossover points are minimal [16]. The corner frequencies of 

the desired filter for the subwoofers were set to 17 Hz and 80 Hz. These corner frequencies were selected 

because 17 Hz is the lower limit of the 20 Hz 1/3-octave band and 80 Hz minimizes the localization 

contribution from the subwoofers [17]. The corner frequencies for the satellite loudspeakers were set to 

80 Hz and 17.23 kHz (44.1 kHz sampling rate/2.56) which is the remainder of the pass-band of interest. 

The upper corner frequency covers most, but not all, of the 16 kHz 1/3-octave band. 
10

Figure 7: Equalization of the sound reproduction system using a Wiener FIR equalization filter. 

In previous work [18], Wiener FIR equalization filters were generated and evaluated in the EER. It 

was shown that good spectral compensation was achieved within the pass-bands and that no audible 

artifacts were produced. Additionally, measurements of the full-path time delay (as described in Section 

4.1) revealed that delay compensation was achieved to within 0.1 ms across all channels of the EER 

sound-reproduction system. However, the resulting Wiener FIR equalization filters required 32k and 8k 

taps for the subwoofer and satellite loudspeakers, respectively. The long filter lengths prevented their use 

in the real-time sound reproduction system, which requires all output channels to be processed 

simultaneously (see Figure 4). In order to obtain equalization filters that can be used in a real-time 

system, the resulting Wiener FIR equalization filters were approximated by reduced-order IIR filters, as 

next discussed. 

3.3 IIR Equalization Filters 

Reduced order IIR surrogates of the Wiener FIR equalization filters, amenable to real-time 

implementation, were generated using the damped Gauss-Newton method for iterative search [19]. Given 

a complex frequency response, this method estimates a stable IIR filter of specified order that 

approximates the associated Wiener FIR equalization filter. Here, the order refers to the numerator and 

denominator polynomials of the Z-domain transfer function representation of the IIR filter. The complex 

frequency response used to estimate the IIR filter was formed from the magnitude response of the target 

Wiener FIR equalization filter and a minimum-phase response. The minimum-phase representation was 

used in lieu of the phase response of the target Wiener FIR equalization filter because it was convenient to 

sum the time delays associated with the filter and the acoustic path, and to process that with a single delay 

line in the AuSIM3D® DSP engine. The minimum-phase response was estimated using the complexcepstrum algorithm [20]. A reconstructed minimum-phase filter is achieved by appropriately windowing 

its cepstrum. 

While it may be obvious, the reduced-order IIR filters should have the same pass-bands for the 

subwoofers and satellites as the Wiener FIR equalization filters upon which they are based. However, 

initial testing indicated that the IIR filter frequency response of the satellite loudspeakers near the 80 Hz 

crossover point was not adequately compensated when those filters were based upon the full bandwidth of 

the Wiener FIR equalization filter (80 Hz – 17.23 kHz). Improved agreement between the desired 

frequency response and the IIR response was achieved by splitting the single IIR into two IIR 

equalization filters for each satellite loudspeaker response. These equalization filters had pass-bands of 80 

Hz - 500 Hz, and 500 Hz – 17.23 kHz, as shown in Figure 8. The DSP system used is not currently 

programmed to permit specification of multiple filters for a single loudspeaker. Therefore, the resulting 

IIR equalization filter pairs for each satellite loudspeaker were summed together into a single IIR 
11

equalization filter. To minimize round-off error, these filters were realized as a cascade of Second-Order 

Sections (SOSs) or “bi-quads” [21]. 

Figure 8: Crossover filter for subwoofers (dashed line), satellite speakers (dotted and dash-dot 

lines), and the desired response across the full frequency range (solid line). 

Undesirable audible behavior (e.g., high frequency ringing) was occasionally observed when 

implementing the IIR equalization filters with the Intel Integrated Performance Primitives (IPP®) DSP 

libraries [22] employed by the real-time AuSIM3D® Engine. To identify any DSP processing issues, the 

IIR equalization filters were first evaluated offline with the same Intel IPP® DSP library functions used in 

the real-time engine. Accordingly, adjustments were made to the filter parameters (e.g., filter order) until 

the filtered signal was free of audible artifacts. 

Figure 9 show the magnitude responses of a Wiener FIR equalization filter (solid) and the 

corresponding IIR surrogate equalization filter (dashed) for satellite loudspeaker 1.5 (top) and subwoofer 

loudspeaker 15L (bottom). The FIR filters shown were obtained using the responses from two centrally 

located microphones. As can be seen, the pass-bands for both the FIR and IIR equalization filters match 

closely. The magnitude responses for the other loudspeakers compare equally well. 

100 101 102 103 104

-100

-90

-80

-70

-60

-50

-40

-30

-20

-10

0

10

Frequency (Hz) Magnitude (dB)

Subwoofer Satellite Satellite Full
12

Figure 9: Magnitude response of the Wiener FIR equalization filter (solid) and the IIR equalization filter (dashed) for 

satellite loudspeaker 1.5 (top) and subwoofer loudspeaker 15L (bottom). 

Replacement of the Wiener FIR equalization filters with surrogate IIR equalization filters, reduced 

the filter order to about 25 SOSs for the subwoofers and 50 SOSs for the satellite loudspeakers. In this 

form, all 31 IIR equalization filters could be processed simultaneously on the DSP engine. 

4 Time-Delay and Gain Compensation 

The two remaining parts of the fixed equalization are time-delay and gain compensation. Like the 

filters, these are determined for each individual loudspeaker. 

4.1 Time-Delay Compensation

The delays used for time delay compensation were estimated from the uncompensated loudspeaker 

impulse responses measured at the central microphone location using a peak detection algorithm [23]. 

Figure 10 shows the detected peaks (dots) using the peak detection algorithm for the uncompensated and 

compensated impulse responses for a satellite loudspeaker (solid) and a subwoofer loudspeaker (dashed). 

As can be seen, the peak detection algorithm accurately determines the first peak in the impulse 

responses. As shown in the bottom plot of Figure 10, the delays can be used to apply time-delay 

compensation such that the onsets of the impulse responses align more closely. Figure 11 shows the 

uncompensated (top) and compensated (bottom) time delays for the satellite (0.5 to 14R) and subwoofer 

(15L to 16R) loudspeakers. The longest time delay of 15.69 ms is associated with the farthest loudspeaker 

(subwoofer 15R), while the shortest delay of 8.8 ms is associated with the closest loudspeaker (satellite 

7R). These are consistent with the installed ranges indicated in the appendix. As can be seen, there is a 

maximum difference of about 6.89 ms, or about 2.4 m at standard sea level conditions, between the 

smallest and largest time delays before time-delay compensation. After compensation, the delay 

difference is reduced to 0.091 ms or about 3 cm. 

10-7 10-6 10-5 10-4 10-3 10-2 10-1 100 101 Magnitude

FIR

IIR

100 101 102 103 104 10-7 10-6 10-5 10-4 10-3 10-2 10-1 100 101

Frequency (Hz) Magnitude
13

Figure 10: Uncompensated and compensated impulse responses for a satellite loudspeaker (solid), 

a subwoofer loudspeaker (dashed), and the corresponding detected peaks (dots). 

Figure 11: Uncompensated and compensated time delay for the satellite (0.5 to 14R) and 

subwoofer (15L to 16R) loudspeakers. 

4.2 Relative Gain Compensation 

The mean sound pressure level (SPL) for each loudspeaker, as measured at the two co-located center 

microphones, varied due to differences in range and installation effects. The mean level was estimated by 

calculating the average of the 1/3-octave band levels within the pass-band of the cross-over filter, i.e. after 

equalization filter compensation. Sufficient headroom in the signal path allowed for an increase in the 

individual loudspeaker gains such that the mean level of each loudspeaker was set to match the highest 

mean level. Figure 12 shows the mean levels for the loudspeakers before (top) and after (bottom) gain 

compensation. The difference between the minimum and maximum uncompensated mean levels for the 

5 7.5 10 12.5 15 17.5 20 22.5 25

-3

-2

-1

0

1

2

3

Uncompensated

Time (ms)

Sat IR

Sub IR

Peaks

5 7.5 10 12.5 15 17.5 20 22.5 25

-3

-2

-1

0

1

2

3

Compensated

Time (ms)

6.0

10.0

14.0

18.0

Loudspeaker Designation Time (ms)

Uncompensated

0.51.52.53L3R4L4R5L5R6L6R7L7R8L8R9L9R10L10R11L11R12L12R13L13R14L14R15L15R16L16R

15.6

15.7

15.8

Loudspeaker Designation Time (ms)

Compensated

0.51.52.53L3R4L4R5L5R6L6R7L7R8L8R9L9R10L10R11L11R12L12R13L13R14L14R15L15R16L16R

6.89 ms (~2.4 m)

0.091 ms (~3 cm)
14

satellites (0.5 to 14R) was about 1.5 dB and for the subwoofers (15L to 16R) was about 0.2 dB. After 

compensation, this was reduced to about 0.05 dB for the satellites and about 0.09 dB for the subwoofers. 

Figure 12: Uncompensated (top) and compensated (bottom) levels of the satellite (0.5 to 14R) and subwoofer (15L to 16R) 

loudspeakers. 

5 Acoustic Performance 

Tests of the EER sound-reproduction system were conducted to assess its acoustic performance. 

Assessments were made based on results of crossover performance, stationary and dynamic VBAP 

performance, maximum level, and spatial uniformity tests. 

5.1 Crossover Performance 

To test the crossover performance, a satellite and subwoofer loudspeaker pair was excited with pink 

noise compensated with the corresponding IIR equalization filters. The sound-reproduction system’s 

capability of positioning a virtual source was not considered in this test. Hence, VBAP was disabled in 

this evaluation. The resulting responses within the 20 Hz – 12.5 kHz 1/3-octave bands are shown in 

Figure 13 for a single satellite loudspeaker 8R, a single subwoofer 15R), and the combined active pair. 

For each 1/3-octave band, the levels shown are the average obtained from two centrally located 

microphones. The plot reveals that no significant increase or decrease in level is observed at the crossover 

frequencies (80 Hz and 500 Hz) when both loudspeakers are active. Furthermore, the minimum-tomaximum level difference of the combined active pair is about 5.5 dB which is consistent with the 

individual loudspeaker compensation results reported in [11]. By conducting this test on other 

loudspeaker pairs, it was found that the crossover performance was comparable. The results of this test 

serve as a benchmark against which the subsequent stationary and dynamic results are compared. 

Uncompensated Mean SPL (dB) 1 dB/Tick

0.51.52.53L3R4L4R5L5R6L6R7L7R8L8R9L9R10L10R11L11R12L12R13L13R14L14R15L15R16L16R

Compensated

Loudspeaker Designation Mean SPL (dB) 1 dB/Tick

0.51.52.53L3R4L4R5L5R6L6R7L7R8L8R9L9R10L10R11L11R12L12R13L13R14L14R15L15R16L16R

~1.5 dB

~0.2 dB

~0.05 dB ~0.09 dB
15

Figure 13: Typical results from the crossover performance test. 

5.2 Stationary Performance 

The stationary performance of the sound-reproduction system is defined here as the system’s ability 

to reproduce the desired magnitude response of a virtual source within a loudspeaker triplet. Hence, 

VBAP was enabled in this evaluation. For the test described here, three loudspeakers were used to create 

a virtual source within the loudspeaker triplet using equal gains for the loudspeakers. This was performed 

by sending the same signal to all loudspeakers, but with individual equalization filters and time delays 

applied. The individual compensated loudspeaker responses for satellite loudspeakers 0.5, 3L, and 3R and 

the compensated virtual source response are shown in Figure 14. For each 1/3-octave band, the levels 

shown are the average obtained from two centrally located microphones. A measure of the flatness of the 

recorded spectra is the minimum-to-maximum level difference, i.e. the difference between the minimum 

and maximum 1/3-octave band levels over the frequency range. The average level difference for the three 

individual satellite loudspeakers is 4.1 dB, while the level difference for the virtual source is about 6.3 

dB. The increased level difference of the latter indicates that the compensation of the individual 

loudspeakers is better than the compensation of their combined output. 

Ideally, the loudspeaker triplet should increase the sound pressure level to three times (9.5 dB) that of 

the individual loudspeakers. Over the frequency range shown, the average 1/3-octave band increase was 

7.7 dB, with a minimum increase of 6.0 dB in the 12.5 kHz band, and a maximum increase of 9.1 dB in 

the 400 Hz band. The reduction is caused by differences between compensated responses of the individual 

loudspeakers. These may be in the form of differences in the magnitude and/or phase response between 

speakers, the latter giving rise to destructive interference. Note that similar behavior was observed in the 

responses measured at the individual microphones. Therefore, this behavior was not a result of averaging 

the two centrally located microphone responses. The narrowband responses of each loudspeaker forming 

the triplet, and their combined response are shown in Figure 15. Magnitude differences between speakers 

are seen over the entire frequency range. Although a minimum phase representation was selected in the 

IIR filter design, destructive interference is also likely to contribute, particularly at high frequencies 

where shorter wavelengths are more affected by phase differences. Results from other loudspeaker triplets 

are comparable. Improvement upon the combined response of the loudspeaker triplet is an area of interest 

in further investigations. 

1/3-Octave Band Center Frequency (Hz) Sound Pressure Level (10 dB/Tick)

202531.540

506380100

1251602002503154005006308001k 1.25k1.6k2k2.5k 3.15k4k5k6.3k8k10k 12.5k

(8R)+(15R) 8R

15R
16

Figure 14: Typical stationary performance test results (broadband). 

Figure 15: Typical stationary performance test results (narrowband). 

5.3 Dynamic Performance 

Considering that the location of virtual sources will generally be moving during an aircraft flyover 

simulation, it is of interest to analyze the dynamic performance of the real-time sound reproduction 

system, that is, the performance through the full DSP path indicated in Figure 4. For this evaluation, a 

virtual source was rotated 360° azimuthally around the EER, at three elevations, over a five-minute 

period. Figure 16 shows the uncompensated (left) and compensated (right) microphone responses of an 

orbiting source at elevations of 10°. Response measurement at elevation angles of 40° and 70° (not 

shown) were comparable. The levels shown are the average obtained from two centrally located 

microphones. For any given elevation and azimuth angle, the sound pressure level (relative to the mean) 

as a function of frequency is a measure of the flatness of the response. Analysis of the uncompensated 

1/3-Octave Band Center Frequency (Hz) Sound Pressure Level (10 dB/Tick)

125160200250315400500630800 1k1.25k1.6k 2k2.5k3.15k 4k

5k6.3k 8k10k12.5k

(0.5)+(3L)+(3R)

0.5

3L

3R

0 2 4 6 8 10 12 14

10-3

10-2

10-1

100

Frequency (kHz) PSD (Pa2/Hz)

(0.5)+(3L)+(3R)

0.5

3L

3R
17

response indicates minimum-to-maximum level differences of about 25 dB (from +15 dB to -10 dB 

relative to the mean). This is largely attributable to the elevated subwoofer responses relative to the 

satellite responses. If the action of dynamically changing the virtual source position degrades the 

compensated performance, then the compensated response should have greater minimum-to-maximum 

level differences than the stationary case considered in the previous section. This is shown not to be the 

case as most level differences are about 6 dB (±3 dB relative to the mean), which is comparable to the 

stationary case (6.3 dB). A slight trend toward increasing difference with increasing elevation angle was 

noted when comparing the respective compensated responses (not shown), although this effect is 

considered minor. 

It is further interesting to note that the spectral shape of the compensated response at any particular 

elevation and azimuth angle bears resemblance to the stationary case. At lower frequencies, the response 

is, on average, higher than the mean and at higher frequencies the response is, on average, lower than the 

mean. 

This test thus verifies that the compensated performance is not degraded by the action of dynamically 

changing the virtual source position. 

Figure 16: Uncompensated (left) and compensated (right) responses for an orbiting source 

at an elevation of 10°. 

5.4 Maximum Spatialized SPL 

The purpose of this test was to determine the maximum SPL the sound-reproduction system can 

produce from a single virtual source. The acoustic energy of the virtual source analyzed in this test was 

equivalent to a single satellite loudspeaker and a single subwoofer loudspeaker. The system was driven by 

band-limited (16 Hz – 10 kHz) pink noise and the responses were measured at the two centrally located 

microphones. The average uncompensated and compensated responses are shown in Figure 17. The 

maximum overall SPL was about 96.4 dB (or about 89.0 dBA) for the uncompensated response and about 

80.4 dB (or about 79.2 dBA) for the compensated response. These results reflect the typical maximum 

overall SPL found at other virtual source locations. The reduction in compensated SPL can be attributed 

to several factors including reduction in subwoofer power when the equalization filters are applied, and 

power limitations of the satellite loudspeakers. Higher overall SPL can be achieved by reducing the 

frequency range of the excitation signal. 
18

Figure 17: Uncompensated and compensated SPLs for a single virtual source. 

5.5 Spatial Uniformity

A legacy mode of operation of the EER is for reproduction over only the ceiling loudspeakers. The 

test conducted here determined the spatial uniformity of the levels generated when all the ceiling 

loudspeakers (4L/R, 5L/R and 6L/R) are simultaneously active in a non-spatialized (non-VBAP) mode. 

The ceiling loudspeakers were driven by band-limited (16 Hz – 10 kHz) pink noise and the responses 

were measured at the seat locations indicated in Figure 18. One set of compensated responses was 

obtained for each IIR equalization configuration (i.e., one response set each for the two-microphone (top) 

or twelve-microphone (bottom) configurations (Figure 19)). The goal was to achieve an overall SPL 

variance within 1 dB at the seat locations. The actual variance achieved was within about 2 dB for the 

two-microphone equalization and within about 3 dB for the twelve-microphone equalization. The 

minimum-to-maximum 1/3-octave band level difference was about 16.5 dB for both equalizations, with a 

maximum variance within a single 1/3-octave band of about 11 dB for the two-microphone equalization 

and about 12.3 dB for the twelve-microphone equalization, both at the 160 Hz band. 

 

Figure 18: Aerial view of the EER with highlighted microphone locations. 

0

10

20

30

40

50

60

70

80

90

100

16202531.540

506380100

1251602002503154005006308001k 1.25k1.6k2k2.5k 3.15k4k5k6.3k8k10k Overall SPL (dB)

1/3-Oct Band Freqs (Hz)

Uncompensated Compensated
19

Figure 19: Compensated SPLs at various seat locations in the EER for a 2 microphone configuration (top) and a 12 

microphone configuration (bottom). 

6 Application Examples 

As indicated in the introduction, the primary function of the EER is for conducting psychoacoustic 

studies of aircraft community noise through simulation of flyover events using recorded [24] or 

synthesized [25–27] aircraft noise. Two examples using flight test recordings are presented for straight 

and level flyovers. In both cases, the reproduced flyover noise was measured at two centrally located 

microphones. 

In the first, a flyover of a Boeing 767 was simulated using a known trajectory and matching sideline 

recording made from a flight test at Wallops Island [28]. The flight test was conducted at very low 

altitude (400 feet above ground level (AGL)), so the recording was scaled to a level more representative 

of that encountered in the community. The top plot of Figure 20 shows the A-weighted SPL time history 

of recorded and reproduced flyover noise. Absolute gain calibration was performed by matching the Aweighted sound exposure level (SELA). Good agreement is seen above the EER noise floor of about 42 

dBA. 

In the second example, a flyover of a Mi-8 helicopter was simulated using a known trajectory and 

matching overhead recording made from a flight test at Eglin Air Force Base [29]. The recording was 

again scaled due to the low altitude (145 feet AGL) at which the test was conducted. The bottom plot of 

Figure 20 shows the C-weighted SPL time history of the recorded and reproduced flyover. C-weighting 

was used here to better represent the low frequency content of helicopter noise, and absolute gain 

calibration was performed by matching the C-weighted sound exposure level (SELC). Excellent 

agreement is seen above the EER noise floor of about 55 dBC. 

0

10

20

30

40

50

60

70

80 SPL (dB)

1D

1G

2C

2F

2H

3D

3G

0

10

20

30

40

50

60

70

80

1/3-Oct Band Freqs (Hz) SPL (dB)

16202531.540

506080100

1251602002503154005006308001k 1.25k1.6k2k2.5k 3.15k4k5k6.3k8k10k Overall
20

Figure 20: Comparison of the SPL time histories for the recorded and reproduced Boeing 767 (top, A-weighted) and Mi-8 

helicopter (bottom, C-weighted) flyovers. 

7 Concluding Remarks 

The acoustic performance of the real-time three-dimensional sound-reproduction system employed in 

the NASA Langley Research Center Exterior Effects Room was evaluated. A method to generate lower 

order IIR equalization filters, as surrogates for the higher order Wiener FIR equalization filters, was 

developed and implemented. The achieved order reduction permitted operation of the IIR equalization 

filters in the real-time sound-reproduction system. The IIR equalization filters compensated for spectral 

colorization, relative gain, and full-path time delay. The performance of the compensated real-time 

system was demonstrated for stationary and dynamic source positions. Excellent comparisons of 

simulated flyovers with recordings demonstrated the unique capabilities of the Exterior Effects Room for 

conducting psychoacoustic tests of aircraft flyover noise. 

Tests were also conducted to evaluate the system performance in other modes of operation. These 

included assessments of the maximum SPL and spatial uniformity. The maximum SPL for the 

compensated system was found to be flatter across 1/3-octave bands than the uncompensated response. 

However, the maximum level was reduced to accomplish this. In the overhead loudspeaker mode, the 

spatial uniformity across a typical seating area was found to be somewhat better when using the twomicrophone equalization than when using the twelve-microphone equalization. 

An area for improvement is in the approach taken for loudspeaker equalization. It was found that 

differences between the compensated responses within a loudspeaker triplet reduced the maximum 

possible level of a virtual source. A possible strategy to address that is to develop virtual source specific 

equalization, rather than the current approach employing equalization specific to individual loudspeakers. 

As with the VBAP gains, such equalizations could be pre-computed for a large but finite number of 

virtual sources at regularly spaced grid points. The filters could be dynamically changed during runtime to 

reflect the current virtual source position, however a strategy to select the nearest equalization would need 

to be employed to avoid the possibility of generating unstable IIR filters through interpolation. Changes 

to the current DSP architecture would be required to implement this approach. In addition, the effect of 

alternative phase representations used in the generation of the IIR equalization filters can be explored. 

10 20 30 40 50

0

20

40

60

80

100 SPL (dBA)

SELA

Flight Test (Scaled) Reproduced Noise Floor

0 10 20 30 40 50 60 70

0

20

40

60

80

100

Time (s) SPL (dBC)

SELC
21

8 Appendix - Installed Speaker Locations

Speaker x Location (m)* y Location (m)* z Location (m)* Range (m)*

0.5 0.0135 4.8165 0.4886 4.8412

1.5 0.0050 4.1948 2.5288 4.8981

2.5 -0.0268 -2.9825 2.8451 4.1220

3L -1.4782 4.5659 -1.0747 4.9181

3R 1.5034 4.5729 -1.0335 4.9234

4L -1.4916 2.1578 3.3120 4.2250

4R 1.5068 2.1796 3.3205 4.2482

5L -1.4986 -0.0118 3.5797 3.8807

5R 1.4853 -0.0393 3.5560 3.8539

6L -1.5146 -2.6515 3.5236 4.6626

6R 1.4968 -2.6460 3.5248 4.6547

7L -0.8095 -2.8625 0.5492 3.0250

7R 0.7874 -2.8578 0.5419 3.0134

8L -2.2088 4.2239 1.3174 4.9453

8R 2.2504 4.2599 1.2846 4.9861

9L -3.5835 2.9424 -1.0297 4.7497

9R 3.5776 3.0662 -1.0462 4.8265

10L -3.4537 2.2867 2.8726 5.0407

10R 3.4401 2.3888 2.8828 5.0844

11L -3.8790 0.6535 1.2083 4.1151

11R 3.8958 0.7291 1.1987 4.1407

12L -3.8974 -1.4630 -0.0795 4.1637

12R 3.8767 -1.3999 -0.0549 4.1221

13L -3.7039 -1.4203 3.2160 5.1067

13R 3.6912 -1.4383 3.2053 5.0958

14L -3.3342 -3.3782 1.8645 5.0996

14R 3.3339 -3.3407 1.8803 5.0804

15L -2.5341 4.4176 -0.8461 5.1626

15R 2.4189 4.6150 -0.8515 5.2796

16L -3.6358 -3.5071 0.4623 5.0727

16R 3.6451 -3.4606 0.4500 5.0463

* Dimensions are relative to the center microphone location (see Figure 2).
22

9 References 

[1] K. P. Shepherd, “The Subjective Evaluation of Noise from Light Aircraft,” NASA CR-2773, 1976. 

[2] D. A. McCurdy and C. A. Powell, “Effects of Duration and Other Noise Characteristics on the Annoyance 

Caused by Aircraft-Flyover Noise,” NASA TP-1386, 1979. 

[3] D. A. McCurdy, “Effects of Sound Level Fluctuations on Annoyance Caused by Aircraft-Flyover Noise,” 

NASA TP-1576, 1979. 

[4] D. A. Mccurdy and C. A. Powell, “Annoyance Caused by Propeller Airplane Flyover Noise,” NASA TP2356, 1984. 

[5] D. A. McCurdy, “Annoyance Caused by Advanced Turboprop Aircraft Flyover Noise, Single-RotatingPropeller Configuration,” NASA TP-2782, 1988. 

[6] J. D. Leatherwood and B. M. Sullivan, “A Laboratory Study of Subjective Annoyance Response to Sonic 

Booms and Aircraft Flyovers,” NASA TM-109113, 1994. 

[7] V. Pulkki, “Virtual Sound Source Positioning Using Vector Base Amplitude Panning,” Journal of the Audio 

Engineering Society (JAES), vol. 45, no. 6, pp. 456–466, 1997. 

[8] V. Pulkki, “Spatial Sound Generation and Perception by Amplitude Panning Techniques,” Helsinki 

University of Technology, Helsinki, Finland, Tech. Rep, 2001. 

[9] J. Busby et al., “3D Model and Tutorial Shop: Free 3D Head Scan Model,” Ten24, 2010. [Online]. 

Available: http://www.ten24.info/index.php/shop/3d-head-scans/free-3d-head-scan-model-52/. [Accessed: 

10-Dec-2012]. 

[10] AuSIM Inc., “Corporate Website,” 2012. [Online]. Available: http://www.ausim3d.com/. [Accessed: 10-

Dec-2012]. 

[11] K. J. Faller II et al., “Acoustic Performance of an Installed Real-Time Three-Dimensional Audio System,” in 

Proceedings of Meetings on Acoustics (POMA), 2011, vol. 11. 

[12] S. J. Elliott et al., “Practical Implementation of Low-Frequency Equalization Using Adaptive Digital 

Filters,” Journal of the Audio Engineering Society (JAES), vol. 42, no. 12, pp. 988–998, 1994. 

[13] M. Karjalainen and T. Paatero, “Equalization of Loudspeaker and Room Responses Using Kautz Filters: 

Direct Least Squares Design,” EURASIP Journal on Advances in Signal Processing, vol. 2007, pp. 1–14, 

2007. 

[14] S. J. Elliott and P. A. Nelson, “Multiple-Point Equalization in a Room Using Adaptive Digital Filters,” 

Journal of the Audio Engineering Society (JAES), vol. 37, no. 11, pp. 899–907, 1989. 

[15] B. Musicus, “Levinson and Fast Choleski Algorithms for Toeplitz and Almost Toeplitz Matrices,” MIT RLE 

Technical Report, no. 538, 1988. 

[16] S. H. Linkwitz, “Active Crossover Networks for Noncoincident Drivers,” Journal of the Audio Engineering 

Society (JAES), vol. 24, no. 1, pp. 2–8, 1976. 
23

[17] E. Winer, The Audio Expert: Everything You Need to Know About Audio. Waltham, MA: Focal Press, 2012, 

p. 696. 

[18] K. J. Faller II et al., “Acoustic Calibration of the Exterior Effects Room at the NASA Langley Research 

Center,” in Proceedings of Meetings on Acoustics (POMA), 2010, vol. 9. 

[19] J. E. Dennis and R. B. Schnabel, Numerical Methods for Unconstrained Optimization and Nonlinear 

Equations. Englewood Cliffs, NJ: Prentice-Hall, 1983, p. 394. 

[20] A. V. Oppenheim and R. W. Schafer, Digital Signal Processing. Englewood Cliffs, NJ: Prentice-Hall, 1975, 

p. 585. 

[21] J. Proakis and D. Manolakis, “Quantization of Filter Coefficients,” in Digital Signal Processing: Principles, 

Algorithms and Applications, 3rd ed., Upper Saddle River, NJ: Prentice-Hall, 2005, pp. 569–582. 

[22] Intel Inc., “Intel Integrated Performance Primitives (IPP®),” 2012. [Online]. Available: 

http://software.intel.com/en-us/articles/intel-ipp/. [Accessed: 10-Dec-2012]. 

[23] X. Fiss and A. Kwasinski, “Automatic Real-Time Electric Guitar Audio Transcription,” in IEEE 

International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2011, pp. 373–376. 

[24] S. A. Rizzi and B. M. Sullivan, “A Three-Dimensional Virtual Simulator for Aircraft Flyover Presentation,” 

International Conference on Auditory Display (ICAD), Boston, MA, pp. 87–90, 2003. 

[25] M. Arntzen et al., “A Framework for Simulation of Aircraft Flyover Noise Through a Non-Standard 

Atmosphere,” 18th AIAA/CEAS Aeroacoustics Conference, Colorado Springs, CO, 2012. 

[26] S. A. Rizzi, B. M. Sullivan, and A. R. Aumann, “Recent Developments in Aircraft Flyover Noise Simulation 

at NASA Langley Research Center,” NATO/AVT TG 158 Specialists’ Meeting on Environmental Noise 

Issues Associated with Gas Turbine Powered Military Vehicles, pp. 17–1 to 17–14, 2008. 

[27] S. A. Rizzi and B. M. Sullivan, “Synthesis of Virtual Environments for Aircraft Community Noise Impact 

Studies,” 11th AIAA/CEAS Aeroacoustics Conference, AIAA 2005-2983, Monterey, CA, 2005. 

[28] G. Fleming et al., “Engine Installation Effects of Four Civil Transport Airplanes: Wallops Flight Facility 

Study,” NASA TM-2003-212433. 

[29] M. E. Watts, D. A. Conner, and C. D. Smith, “Joint Eglin Acoustics Week III Data Report,” NASA/TM2010-216206. 
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Technical Memorandum

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Acoustic Performance of a Real-Time Three-Dimensional 

Sound-Reproduction System

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 6. AUTHOR(S)

Faller, Kenneth J., II; Rizzi, Stephen A.; Aumann, Aric R.

 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)

NASA Langley Research Center

Hampton, VA 23681-2199

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National Aeronautics and Space Administration

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14. ABSTRACT

The Exterior Effects Room (EER) is a 39-seat auditorium at the NASA Langley Research Center and was built to support psychoacoustic 

studies of aircraft community noise. The EER has a real-time simulation environment which includes a three-dimensional 

sound-reproduction system. This system requires real-time application of equalization filters to compensate for spectral coloration of the 

sound reproduction due to installation and room effects. This paper describes the efforts taken to develop the equalization filters for use in 

the real-time sound-reproduction system and the subsequent analysis of the system’s acoustic performance. The acoustic performance of the 

compensated and uncompensated sound-reproduction system is assessed for its crossover performance, its performance under stationary and 

dynamic conditions, the maximum spatialized sound pressure level it can produce from a single virtual source, and for the spatial uniformity 

of a generated sound field. Additionally, application examples are given to illustrate the compensated sound-reproduction system 

performance using recorded aircraft flyovers. 

15. SUBJECT TERMS

Acoustic performance; Digital equalization filters; Real-time sound reproduction system; Three-dimensional sound simulation; 

Vector-base amplitude panning (VBAP)

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